Algorithm REF  is a procedure to obtain multiple samples of the random variable \(r(s,a)+\gamma V_{cpt}(s^{\prime })\) .
These samples are then used to estimate \(\rho _{cpt}(r(s,a)+\gamma V_{cpt}(s^{\prime }))\)  (since \(V_{cpt}(s) = \sum _a \pi (\cdot |s)Q_{cpt}(s)\) ).
This way to estimate the CPT-value of a random variable was proposed in [1]}, and was shown to be asymptotically consistent.
In order to obtain these estimates in a privacy-preserving manner, we use Algorithm REF  to determine the quantum of noise that needs to be added for each action at any state.
